Stay away, unless you really like sheikh-jarrah. Convenient transfers to Ramallah, Bethlehem, and Nablus. Sometimes these transfers may be made by courteous drivers, with guns, with you travelling in luxury in the trunk of the car.
Sheikh Jarrah is also a 2 minute walk from Maalot Dafna, is where they say R. Shimon's kever is, and is only a few minutes from the old city.
Shchem is easily over an hour away, and that's without traffic.
Let's not make it out to be so bad.